How Do You Derive Lagrange Equations for a Particle on a Sphere?

[ehrenfest]

Homework Statement

A particle moves on the surface of a sphere. Write down the Lagrange equations.

Homework Equations

The Attempt at a Solution

So since it is a free particle, there is no V in the Lagrangian, correct?

So L = T and I can write:

$$L = 1/2 m (R^2 \cos^2 \phi \dot{ \theta}^2 + R^2 \dot{\theta}^2)$$

phi is the azimuthal angle and theta is the polar angle

Is that all correct? If so, I only need to plug that into the EL equations, right?

 

[lebashad]

hi!
if you expressed x,y and Z in cordonnée spherical I believe that correct